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arXiv 2202.07027gr-qc
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共形和非共形耦合的暗能量矢量场模型

Conformally and Disformally Coupled Vector field Models of Dark Energy

Gabriel Gómez

AI总结:

本研究构建了与暗物质共形和非共形耦合的暗能量矢量场模型,推导了相互作用项的广义协变形式,发现新的标度解和稳定吸引子可驱动宇宙晚期加速膨胀,并分析了耦合对宇宙演化的定量影响及不稳定性条件。

摘要:

通过共形或非共形变换与暗物质耦合的标量场产生了一类广义的标量-张量理论,该理论在宇宙学背景下展现出丰富的现象学特征。尽管文献中已针对标量场对这一可能性开展了全面研究,但矢量场的相关研究却鲜有涉及。因此,我们构建了基于与暗物质共形和非共形耦合的矢量场的模型,并以独立于引力理论的方式明确推导了相互作用项的广义协变形式,该结果可应用于广义矢量-张量理论。\n为具体起见,我们采用带有矢量指数势的标准Proca理论来描述矢量-张量部分,并假设若干特定的耦合函数,通过动力系统技术研究宇宙学背景动力学。尽管我们为基础理论选择了这种极简形式,但由于新型相互作用的存在,与非耦合情形相比,参数空间得到了极大丰富,为矢量运动方程带来了新的解分支。因此,根据与共形和非共形函数相关的耦合参数的不同,相空间中可以存在不同的轨迹。\n在此基础上,我们发现了新出现的矢量-暗物质标度解,以及能够驱动宇宙晚期加速膨胀的新的稳定吸引子点。作为对不稳定性问题的初步检验,我们推导了在更一般的理论框架下避免经典不稳定性的通用条件。我们还进行了数值计算,以更定量地研究共形和非共形耦合对宇宙学背景演化的影响。这些效应主要取决于耦合参数的强度,在某些特定情况下还取决于其相关符号。

英文摘要:

Scalar fields coupled to dark matter by conformal or disformal transformations give rise to a general class of scalar-tensor theories which leads to a rich phenomenology in a cosmological setting. While this possibility has been studied comprehensively in the literature for scalar fields, the vector case has been hardly treated. We build hence models based on vector fields conformally and disformally coupled to dark matter and derive explicitly the general covariant form of the interaction term in an independent way of the gravity theory, whereby this result can be applied to general vector-tensor theories. For concreteness, the standard Proca theory with a vector exponential potential is taken to describe the vector-tensor sector, and some specific coupling functions are assumed to study the cosmological background dynamics by dynamical system techniques. Despite of choosing such a minimalist form for the underlying theory, the parameter space is considerably enriched compared to the uncoupled case due to the novel interactions, leading to new branches of solutions for the vector equation of motion. Thus, different trajectories can exist in phase space depending on the coupling parameters associated to the conformal and disformal functions. From here, new emerging vector-dark matter scaling solutions, and renewed stable attractor points are found to drive the late-time accelerated expansion of the universe. As a first examination about instabilities issues, we derive general conditions to avoid classical instabilities in a more general setup of the theory. Numerical calculations are performed as well to investigate more quantitatively the impact of the conformal and disformal couplings on the cosmological background evolution. These effects depend essentially on the strength on the coupling parameters and, in some specific cases, on their associated signs.

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